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A microburst can be modelled by releasing a volume of fluid that is slightly heavier than the ambient fluid, allowing it to fall onto a horizontal surface. Vorticity develops on the sides of this parcel as it descends and causes it to roll up into a turbulent vortex ring which impinges on the ground. Such a model exhibits many of the features of naturally occurring microbursts which are a hazard to aviation. In this paper this model is achieved experimentally by releasing a volume of salt water into fresh water from a cylindrical dispenser. When care is taken with the release the spreading rate of the surface outflow is measurable and quite repeatable despite the fact that the flow is turbulent. An elementary numerical approximation to this model, based on inviscid vortex dynamics, has also been developed. A scaling law is proposed which allows experiments with different fluid densities to be compared with each other and with the numerical results. More importantly the scaling law allows us to compare the model results with real microbursts.

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Abstract

Drag control using a newly developed spanwise opposed wall-jet forcing (SOJF) method is studied via direct numerical simulation of the incompressible Navier–Stokes equations in a turbulent channel flow (at the friction Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}=180$ and 550). SOJF is characterized by three control parameters: the forcing amplitude $A^{+}$, the spanwise spacing $\unicode[STIX]{x1D706}^{+}$ and the wall-jet height $y_{c}^{+}$ ($+$ indicates viscous scaling). At $Re_{\unicode[STIX]{x1D70F}}=180$, notable drag reduction is achieved for wide ranges of $A^{+}$, $\unicode[STIX]{x1D706}^{+}$ and $y_{c}^{+}$, with an optimal drag reduction of approximately 19 % found for $A^{+}\approx 0.015$, $\unicode[STIX]{x1D706}^{+}\approx 1200$ and $y_{c}^{+}\approx 30$. The drag reduction results from mergers of numerous low-speed typical individual streaks together by the wall jets, so that the slope of the merged streak envelope and hence the streak strength are reduced below the critical values required for streak instability as well as for transient growth; consequently, the generation of drag inducing near-wall streamwise vortices is suppressed. Through analysis using the FIK identity (Fukagata et al. Phys. Fluids, vol. 14 (11), 2002, pp. L73–L76) in combination with the triple decomposition and the spanwise wavenumber spectrum of the Reynolds shear stress, we find that the control significantly decreases skin friction due to the small scale random turbulent structures (from 75 to 23 % for the optimal case), but injects a dominant contribution at the forcing scale (approximately 34 %). As $A^{+}$ or $y_{c}^{+}$ increases, the drag reduction degrades due to the downwash near the initiation of the forcing wall jet. The energy input required for the excitation is found to be small, yielding a 17 % net power saving for the optimal control case. To determine the $Re$ dependence of the drag reduction, the control strategy is further validated at a higher $Re_{\unicode[STIX]{x1D70F}}=550$. If the control parameters are kept the same as at $Re_{\unicode[STIX]{x1D70F}}=180$ (i.e. $A^{+}\approx 0.015$, $\unicode[STIX]{x1D706}^{+}\approx 1200$, $y_{c}^{+}\approx 30$), the drag reduction decreases to 10 %; however, interestingly, with modestly changed parameters ($A^{+}\approx 0.018$, $\unicode[STIX]{x1D706}^{+}\approx 1700$, $y_{c}^{+}\approx 50$), drag reduction increases to about 15 %. This additional drag reduction results from the further suppression of turbulent structures in the buffer and log regions. This result, therefore, suggests prospects for drag reduction at even higher $Re$ via a proper choice of the SOJF parameters.

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The effect of Reynolds number (Reτ) on drag reduction using spanwise wall oscillation is studied through direct numerical simulation of incompressible turbulent channel flows with Reτ ranging from 200 to 2000. For the nondimensional oscillation period T+ = 100 with maximum velocity amplitude A+ = 12, the drag reduction (DR) decreases from 35.3% ± 0.5% at Reτ = 200 to 22.3% ± 0.7% at Reτ = 2000. The oscillation frequency ω+ for maximum DR slightly increases with Reτ, i.e., from ω+ ≈ 0.06 at Reτ = 200 to 0.08 at Reτ = 2000, with DRmax=23.2%±0.6%. These results show that DR progressively decreases with increasing Reτ. Turbulent statistics and coherent structures are examined to explain the degradation of drag control effectiveness at high Reτ. Fukagata, Iwamoto, and Kasagi analysis in combination with the spanwise wavenumber spectrum of Reynolds stresses reveals that the decreased drag reduction at higher Reτ is due to the weakened effectiveness in suppressing the near-wall large-scale turbulence, whose contribution continuously increases due to the enhanced modulation and penetration effect of the large-scale and very large-scale motions in the log and outer regions. Both the power-law model (DR∝Reτ−γ) and the log-law model [DR = f(Reτ, ΔB), where ΔB is the vertical shift of the log-law intercept under control] are examined here by comparing them with our simulation data, from these two models we predict more than 10% drag reduction at very high Reynolds numbers, say, Reτ = 105.

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